TY - JOUR

T1 - Traveling wave solutions of advection-diffusion equations with nonlinear diffusion

AU - Monsaingeon, L.

AU - Novikov, A.

AU - Roquejoffre, J. M.

N1 - Funding Information:
L.M. would like to thank the PREFERRED French ANR project and NSF grant DMS-0908011 for financial support, Penn State University and Stanford University for their hospitality. A.N. was supported by the NSF grant DMS-0908011.

PY - 2013

Y1 - 2013

N2 - We study the existence of particular traveling wave solutions of a nonlinear parabolic degenerate diffusion equation with a shear flow. Under some assumptions we prove that such solutions exist at least for propagation speeds cε]C*,+∞[, where C*>0 is explicitly computed but may not be optimal. We also prove that a free boundary hypersurface separates a region where u=0 and a region where u>0, and that this free boundary can be globally parametrized as a Lipschitz continuous graph under some additional non-degeneracy hypothesis; we investigate solutions which are, in the region u>0, planar and linear at infinity in the propagation direction, with slope equal to the propagation speed.

AB - We study the existence of particular traveling wave solutions of a nonlinear parabolic degenerate diffusion equation with a shear flow. Under some assumptions we prove that such solutions exist at least for propagation speeds cε]C*,+∞[, where C*>0 is explicitly computed but may not be optimal. We also prove that a free boundary hypersurface separates a region where u=0 and a region where u>0, and that this free boundary can be globally parametrized as a Lipschitz continuous graph under some additional non-degeneracy hypothesis; we investigate solutions which are, in the region u>0, planar and linear at infinity in the propagation direction, with slope equal to the propagation speed.

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U2 - 10.1016/j.anihpc.2012.11.003

DO - 10.1016/j.anihpc.2012.11.003

M3 - Article

AN - SCOPUS:84881181798

SN - 0294-1449

VL - 30

SP - 705

EP - 735

JO - Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis

JF - Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis

IS - 4

ER -